Digital electronic systems for transmitting static or moving images or for processing acoustical recordings, radar echoes and seismic signals necessarily operate on signals defined in a two-dimensional domain, i.e. in time and space. Such signal-processing systems may include recursive filters, which considerably reduces the amount of computations while also providing a high application flexibility with respect to nonrecursive-filtering techniques. To augment processing efficiency, the pulse responses of the recursive filters are defined only in a half-plane of the space-time domain; the restriction of the pulse response does not preclude filter operation according to any specified frequency-response function. Although recursive filtering in a half-plane of the space-time domain is theoretically possible, conventional two-dimensional filters obtain good approximations only in a quadrant of the domain area. In the processing of images, constraining the signal response to a single quadrant achieves acceptable noise reduction or image restoration, but this technique is not suitable for the study of wave propagation through a homogeneous medium: a wavefront generated by a source in such a medium produces in a linear array of sensors a response defined by a hyperbola of the space-time domain, while a recursive filter with a pulse response defined only in a single quadrant is generally incapable of processing hyperbolically arrayed input data. In lieu of two-dimensional recursive filters effective in a half-plane, separate filtering has been proposed wherein the time variable is filtered recursively and the space variable is processed in a transversal filter. Such separate processing is likely to approximate the hyperbolic pulse response with a parabolic one, the symmetry of the response being preserved and times being roughly equivalent to those obtained with a two-dimensional recursive filter of like order. However, the simplification inherent in a parabolic approximation is too drastic to produce reliable results even by filters of a very high order.